When a certain basketball player takes his first shot in a game he succeeds with prob. 1/3. If he misses his first shot, he loses confidence and his second shot will go with prob. 1/4. If he misses his first 2 shots, his third shot will go with pro. 1/5. If he misses his first 3 shots, his fourth shot will go with prob. 1/6. If he misses his first 4 shots, the coach will remove hom from the game. Assume that the player keeps shooting until he succeeds or he is removed from the game. Let X denote the number of shots he misses until his first success or until he is removed from the game. Required:
a. Compute the p. m.f. of X
b. Compute E[X]

X : 0 1 2 3 4

P(x) : _ 0.333_0.167 _0.100_0.067__0.333

E(X) = 1.9

Step-by-step explanation:

From the question above:

X ; number of misses

For :

X = 0 ; P(X = 0) = 1/3 = 0.333

X = 1 ; misses first ; succeeds on second

P(X = 1) = 2/3 * 1/4 = 2/12 = 1/6 = 0.167

X = 2 ; misses first, misses second, succeeds on third

P(X = 2) = 2/3 * (1 - 1/4) * 1/5 = 2/3*3/4*1/5 = 6/60 = 1/10 = 0.10

X = 3 :misses first, misses second, misses third succeeds on fourth

P(X = 3) = 2/3 * 3/4 * (1 - 1/5) * 1/6 = 2/3*3/4*4/5*1/6 = 24/360 = 0.067

X= 4

P(X =4) = 2/3 * 3/4 * 4/5 * 5/6 = 120/ 360 = 1/3 = 0.333

X : 0 1 2 3 4

P(x) : _ 0.333_0.167 _0.100_0.067__0.333

E(X) :

Σx*p(x) = (0*0.333) + (1*0.167) + (2*0.100) + (3*0.067) + (4*0.333)

0 + 0.167 + 0.2 + 0.201 + 1.332

= 1.9

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

~

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: