Question

A stockbroker knows from past experience that the probability that a client owns stocks is 0.60 and the probability that a client owns bonds is 0.50. The probability that a client owns stocks if he/she already owns bonds is 0.06. Given that a client owns stock, Calculate the probability (as a decimal) that he/she owns bonds?

Answer 1

"0.07" is the appropriate answer.

Explanation:

The given values are:

P(Stock),

= 0.60

P(Bond),

= 0.50

P(Bond | Stock),

= 0.06

Now,

The P(Stock | Bond) will be:

⇒
`P(Stock|Bond)= (P(Stock \ and \ Bond))/(P(Bond))`

or,

⇒
`P(Stock|Bond)=(P(Bond|Stock).P(Stock))/(P(Bond))`

On substituting the given values, we get

⇒
`=(0.06* 0.60)/(0.50)`

⇒
`=(0.036)/(0.50)`

⇒
`=0.07`