 # Basic Joint Probability Question......?

An investor has determined that 85% of stocks in her portfolio have paid a dividend and 40% have announced a stock split. If 95% of the stocks have paid a dividend and/or announced a stock split, the joint probability of paying a dividend and announcing a stock split is closest to: A. 10% B. 30% C. 45% D. 55%

Where’d you get that question from? I was thinking it was (.85) * (.40) = .34 But, I guess that can’t be right?

Eric, when I look up joint probability, the formula I see says to multiply (.85) * (.40). However, that is not one of the choices. So, I’m a little confused.

What’s wrong with 0.30? P(Dividends or Splits) = P(Dividends) + P(Splits) - P(Dividends and Splits) 0.95 = 0.40 + 0.85 - P(Dividends and Splits) P(Dividends and Splits) = 0.30

I thought that equation was used for only calculating the probability that only one of the two events occur.

P(Dividends or Splits) = P(Dividends) + P(Splits) - P(Dividends and Splits) This means Dividends or Splits but not both, which is same as saying 95% of the stocks have paid a dividend and/or announced a stock split.

Here’s what I’m thinking: The question asks for joint probability, which normally would entail multiplication (.85 x .4) = .34. The CLOSEST answer to .34 is .3. I am also thinking what Dreary came up with, which is basically a rearranging of the additional rule: P(Dividends or Splits) = P(Dividends) + P(Splits) - P(Dividends and Splits) 0.95 = 0.40 + 0.85 - P(Dividends and Splits) P(Dividends and Splits) = 0.30 Both answers that I came up with are B, but for different reasons. In this case it’s not a perfect science, that’s why I wanted feedback from others.

If you want percentage of your stocks which paid Dividends but had no Splits, plus the percentage of your stocks that had Splits but not paid Dividends, that will be 0.65.

eric23 Wrote: ------------------------------------------------------- > Where’d you get that question from? > > I was thinking it was (.85) * (.40) = .34 > > But, I guess that can’t be right? Eric23 solution is applied only when event “paid dividend” and “stock split” are independent events. And actually they are independent events by sense, right? I’m not sure! Dreary Wrote: ------------------------------------------------------- > What’s wrong with 0.30? > > P(Dividends or Splits) = P(Dividends) + P(Splits) > - P(Dividends and Splits) > 0.95 = 0.40 + 0.85 - P(Dividends and Splits) > P(Dividends and Splits) = 0.30 The formula Dready used correct when P(paid dividend) = .85 and P(stock split) = 0.40 of this case. But if the question say P(Dividends) = .55 and P(Splits) = 0.40 the formula P(Dividends or splits) = P(Dividends) + P(Splits) - P(Dividends and Splits) is nothing sure for the case. So i think the right understand should be “paid dividends” and “stock splits” are independent event, then using multiplication P(Dividends and Splits) = P(Dividends) * P(Splits)

Make sure you account for stocks that are neither Dividend paying nor having Splits. If you say 0.85 * 0.40 = 0.34, then you are ignoring stocks that are neither. Those actually represent 5% of the stocks: P(No Dividend and No Splits) = 1 - P(Dividends) - P(Splits) + P(Dividends and SPLITS) = 1 - 0.85 - 0.4 + 0.30 = 5%

You have 100 stocks: 85 of them have paid dividends 40 of them have had splits 95 of them either paid dividends or had splits or both 5 of them are dull stocks (they didn’t pay dividends no had splits) Now do the math.

Draw the Venn Diagram (those overlapping circles) and label stuff.

Dreary, maybe i am so serious misunderstand but here my case Total: 100 40 paid dividends 30 splits 30 neither dividends nor splits 70 either dividends or splits Yr formula: P(dividends and splits) = 0.4 + 0.3 - 0.7 = 0

An investor has determined that 85% of stocks in her portfolio have paid a dividend and 40% have announced a stock split. If 95% of the stocks have paid a dividend and/or announced a stock split, the joint probability of paying a dividend and announcing a stock split is closest to: P(A or B)= P(A)+P(B)-P(A and B) 0.95= (0.85) + (0.4)- P(A and B) hence: P(A and B)=0.85 + 0.4 - 0.95= 0.30=30%

Thu Thuy, > Yr formula: P(dividends and splits) = 0.4 + 0.3 - 0.7 = 0 In this case 0.7 is NOT "70 either dividends or splits ", but rather "70 are BOTH dividends and splits " Also the formula should say: Yr formula: P(dividends *or* splits) = 0.4 + 0.3 - 0.7 = 0

Thanks Dreary for yr explain! I’ve understood already! I accessed the problem too serious and complicated then going wrong direction. Dreary Wrote: ------------------------------------------------------- > Thu Thuy, > > Yr formula: P(dividends and splits) = 0.4 + 0.3 > - 0.7 = 0 > > In this case 0.7 is NOT "70 either dividends or > splits ", but rather "70 are BOTH dividends and > splits " Also the formula should say: > > Yr formula: P(dividends *or* splits) = 0.4 + 0.3 - > 0.7 = 0