Question

In a certain game of? chance, a wheel consists of 42 slots numbered? 00, 0,? 1, 2,..., 40. To play the? game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. Complete parts? (a) through? (c) below. ?(a) Determine the sample space. Choose the correct answer below. A. The sample space is? {00}. B. The sample space is? {00, 0,? 1, 2,..., 40?}. C. The sample space is? {00, 0}. D. The sample space is? {1, 2,..., 40?}. ?(b) Determine the probability that the metal ball falls into the slot marked 7. Interpret this probability. The probability that the metal ball falls into the slot marked 7 is nothing. ?(Round to four decimal places as? needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. ?(Type a whole? number.) A. If the wheel is spun 1000? times, it is expected that exactly nothing of those times result in the ball not landing in slot 7. B. If the wheel is spun 1000? times, it is expected that about nothing of those times result in the ball landing in slot 7. ?(c) Determine the probability that the metal ball lands in an odd slot. Interpret this probability. The probability that the metal ball lands in an odd slot is nothing. ?(Round to four decimal places as? needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. ?(Type a whole? number.) A. If the wheel is spun 100? times, it is expected that exactly nothing of those times result in the ball not landing on an odd number. B. If the wheel is spun 100? times, it is expected that about nothing of those times result in the ball landing on an odd number.

Answer 1

There are 42 numbers in the slot, so if a metal ball is spun around the wheel it can fall into any of these 42 numbers.

(a) Therefore, the sample space is B. {00, 0, 1, 2,..., 40}.

(b) There are 42 numbers in the slot. So, the probability of each number have an equal probability of the metal ball into that slot i.e, 1/42.

Probability that the metal ball falls into the slot marked 7= 1/42= 0.0238.

A. If the wheel is spun 1000 times, it is expected that exactly 976 of those times result in the ball not landing in slot 7.

B. If the wheel is spun 1000 times, it is expected that about 24 of those times result in the ball landing in slot 7.

(c) from numbers 0 to 40 there are 20 odd numbers in it, also 00 is also not an odd number. Hence, in the given sample space of 42 numbers, we have 20 odd numbers.

The probability that the metal ball lands in an odd slot is = 20/42= 0.4762.

A. If the wheel is spun 100 times, it is expected that exactly 52 of those times result in the ball not landing on an odd number.

B. If the wheel is spun 100 times, it is expected that about 48 of those times result in the ball landing on an odd number.