Question

Based on their analysis of the penalty kicks, the authors of the paper gave the following probability estimates.

P(L) = 0.493

P(B|L) = 0.142

P(C) = 0.093

P(B|C) = 0.333

P(R) = 0.414

P(B|R) = 0.126

(a)

For each of the given probabilities, choose a sentence giving an interpretation of the probability in the context of this problem.

P(L) = 0.493

The probability that the goalkeeper stays in the center.

The probability that the goalkeeper blocks the shot.

The probability that the goalkeeper jumps to the left.

The probability that the kicker scores the shot.

The probability that the goalkeeper jumps to the right.

P(C) = 0.093

The probability that the goalkeeper stays in the center.

The probability that the goalkeeper blocks the shot.

The probability that the goalkeeper jumps to the left.

The probability that the kicker scores the shot.

The probability that the goalkeeper jumps to the right.

P(R) = 0.414

The probability that the goalkeeper stays in the center.

The probability that the goalkeeper blocks the shot.

The probability that the goalkeeper jumps to the left.

The probability that the kicker scores the shot.

The probability that the goalkeeper jumps to the right.

P(B|L) = 0.142

The probability that, given that the kick was blocked, the goalkeeper stays center.

The probability that, given that the goalkeeper jumps to the right, the kick was blocked.

The probability that, given that the goalkeeper jumps to the left, the kick was blocked.

The probability that, given that the goalkeeper jumps to the right, the kick was not blocked.

The probability that, given that the goalkeeper stays in the center, the kick was blocked.

P(B|C) = 0.333

The probability that, given that the kick was blocked, the goalkeeper stays center.

The probability that, given that the goalkeeper jumps to the right, the kick was blocked.

The probability that, given that the goalkeeper jumps to the left, the kick was blocked.

The probability that, given that the goalkeeper jumps to the right, the kick was not blocked.

The probability that, given that the goalkeeper stays in the center, the kick was blocked.

P(B|R) = 0.126

The probability that, given that the kick was blocked, the goalkeeper stays center.

The probability that, given that the goalkeeper jumps to the right, the kick was blocked.

The probability that, given that the goalkeeper jumps to the left, the kick was blocked.

The probability that, given that the goalkeeper jumps to the right, the kick was not blocked.

The probability that, given that the goalkeeper stays in the center, the kick was blocked.

(b)

Use the given probabilities to construct a hypothetical 1,000 table with columns corresponding to whether or not a penalty kick was blocked and rows corresponding to whether the goalkeeper jumped left, stayed in the center, or jumped right. (Round your answers to the nearest integer.)

Blocked (B) Not Blocked (not B) Total

Goalkeeper jumped left (L)

Goalkeeper stayed center (C)

Goalkeeper jumped right (R)

Total 1,000

(c)

Use the table to calculate the probability that a penalty kick is blocked.

Answer 1

P(L) = 0.493 The probability that the goalkeeper jumps to the left.

P(C) = 0.093 The probability that the goalkeeper stays in the center.

P(R) = 0.414 The probability that the goalkeeper jumps to the right.

P(B|L) = 0.142 The probability that, given that the goalkeeper jumps to the left, the kick was blocked.

P(B|C) = 0.333 The probability that, given that the goalkeeper stays in the center, the kick was blocked

P(B|R) = 0.126 The probability that, given that the goalkeeper jumps to the right, the kick was blocked.

	Blocked	Not blocked	total
Goalkeeper jumped left	70	423	493
Goalkeeper stayed center	31	62	93
Goalkeeper jumped right	52	362	414
total	153	847	1000

P(penalty kick is blocked)=153/1000=0.153