91影视

The problem deals with the probability of two persons $A$and $B$answering correctly on a $10$question exam.

Probability of ' $A$ ' answering one question correctly,$P\left(A\right)=0.7$

The probability of success, that is, both $A$and $B$answering a question correctly is given by $p(A鈭�B)=p\left(A\right)脳\mathrm{p}\left(B\right)$

$=0.7脳0.4$

$=0.28.$

Let $X$denotes the number of questions that are answered correctly by both $A$and $B$on a $10$question exam.

Here,$X~Binom(n=10,p=0.28)$

The expected value is found as follows.

$E\left(X\right)=np$

$=10脳0.28$

We get,

$=2.8.$

The expected number of correctly answered questions by both $A$and$B$on a $10$question exam is $2.8.$

The problem deals with the probability of two persons $A$and $B$answering correctly on a $10$question exam.

Probability of ' $B$' answering one question correctly,$P\left(B\right)=0.4.$

The probability that either $A$or $B$answers a question correctly is given below.

$P(A鈭�B)=P\left(A\right)+P\left(B\right)-P(A鈭�B)$

$=0.7+0.4-0.28$

We get,

$=0.82$.

Let$X$ denotes the number of questions that are answered correctly by either $A$or $B$on a$10$question exam.

Here, $X~Binom(n=10,p=0.82)$

Then, the variance of the number of questions correctly answered by either $A$or $B$is given by,

$Var\left(X\right)=np(1-p)$

$=10脳0.82脳(1-0.82)$

$=1.476$

The variance for the number of correctly answered questions by either $A$or $B$is $1.476.$