1 Answer

Dickon Reed · Answer 1 · 2022-12-08T14:50:31+0000

Given:

For two events X and Y,

P(X)=(2)/(3)

P(Y)=(2)/(5)

P(X|Y)=(1)/(5)

To find:

The probabilities
$P(Y\cap X), P(Y)\cdot P(X)$ .

Solution:

Using the conditional probability:

$P(X|Y)=(P(Y\cap X))/(P(Y))$

$P(X|Y)* P(Y)=P(Y\cap X)$

Substituting the given values, we get

$(1)/(5)* (2)/(5)=P(Y\cap X)$

$(2)/(25)=P(Y\cap X)$

And,

P(Y)* P(X)=(2)/(5)* (2)/(3)

P(Y)* P(X)=(4)/(15)

Therefore, the required probabilities are
$P(Y\cap X)=(2)/(25)$ and
.

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