Kim and Susan are playing a tennis match where the winner must win 2 sets in order to win the match. For each set, the probability that Kim wins the set is 0.55. The probability of Kim winning the set is not affected by who has won any previous sets.

a) The probability that Kim wins the match is 0.5747

b)The probability that Kim wins the match in exactly 2 sets is 0.3025

c) The probability that 3 sets are played is 0.495

Step-by-step explanation:

P(Kim Wins)=0.55

P(Susan Wins)=1-0.55=0.45

The possible outcomes are:

KSK,KSS,SKK,SKS,KK,SS

(a) Kim's wins:

P(KK)+P(KSK)+P(SKK)

P(Kim wins first two sets) P(KK)=0.55×0.55=0.3025

P(Kim wins first set, Susan wins second set, Kim wins third set)

P(KSK)=0.55×0.45×0.55≈0.1361

P(Susan wins first set, Kim wins second and third set)

P(SKK)= 0.45×0.55×0.55≈0.1361

Therefore:

P(Kim wins)

= 0.3025+0.1361+0.1361=0.5747

b) Kim wins the match in exactly 2 sets

P(Kim wins first two sets) P(KK)=0.55×0.55=0.3025

(c) 3 sets are played

For three sets to be played, the possible events are:

KSK,KSS,SKK,SKS

P(Kim wins first set, Susan wins second set, Kim wins third set)=

P(KSK)=0.55×0.45×0.55≈0.1361

P(Susan wins first set, Kim wins second and third set)= P(SKK)=0.45X0.55X0.55=0.1361

P(Kim wins first set, Susan wins second and third set)=

P(KSS)=0.55×0.45×0.45≈0.1114

P(Susan wins first set, Kim wins second set and Susan wins third set)=

P(SKS)=0.45×0.55×0.45≈0.1114

Therefore:

P(3 sets are played)

=0.1361+0.1361+0.1114+0.1114

=0.495

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step-by-step explanation:

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: