We have two coins, a and b. for each toss of coin a, we obtain heads with probability 1/2 ; for each toss of coin b, we obtain heads with probability 1/3 . all tosses of the same coin are independent. we toss coin a until heads is obtained for the first time. we then toss coin b until heads is obtained for the first time with coin b. the expected value of the total number of tosses is:

The expected value is 5.

Step-by-step explanation:

As we can see, X=Y+Z. Then, by the linearity of the expected value operator, we have that

Observe that Y and Z have countable sets of outcomes (1,2,3,....) then,

,

,

Then:

Observe that, by the geometric series formula:

Therefore

Finally, E(X)=E(Y)+E(Z)=2+3=5.

none of the option is correct.

step-by-step explanation:

it says to find which expression equals 9^3 sqrt 10 = ?

9^3 sqrt 10 = 729 sqrt 10.

checking option a. 5 sqrt 10 + 4 sqrt 10

5 sqrt 10 + 4 sqrt 10

= 9 sqrt 10.

checking option b. 5^3 sqrt 10 + 4^3 sqrt 10

5^3 sqrt 10 + 4^3 sqrt 10

= 125 sqrt 10 + 64 sqrt 10

= 189 sqrt 10.

checking option c. 5 sqrt 10 + 4^3 sqrt 10

5 sqrt 10 + 4^3 sqrt 10

= 5 sqrt 10 + 64 sqrt 10

= 69 sqrt 10.

checking option d. 5^3 sqrt 10 + 4 sqrt 10

5^3 sqrt 10 + 4 sqrt 10

= 125 sqrt 10 + 4 sqrt 10

= 129 sqrt 10.

hence, none of the option is correct.

47.28 or 47.2857143

step-by-step explanation:

you just divide 331 by 7 and you get that answer. ( i think so tho)