Five cards are dealt at random from a well shuffled deck of 52 playing cards. Fi

Question

Five cards are dealt at random from a well shuffled deck of 52 playing cards. Find the probab.hty that: All are spades. Exactly two are hearts. Exactly three are spades All are black. At least one card is king. Tossing a coin 10 times find the probability of getting exactly 4 tails. Find the probability of getting at least 4 tails for tossing a coin 15 times An airliner wants to know the probability of on time flights for its flights 215 from Orlando to LA. It selects 20 flights randomly. If 92% of the flights are on time, Find the probability that exactly 6 flights are on time, Find the probability that at least 3 flights are on times. If 80% of smokers started smoking before turning 18 years old, and 11 smokers 18 or older are randomly selected find the probability that exactly 7 of them started smoking before 18 years of age Find the probably that at least 7 of them started smoking before 18 years of age

Explanation / Answer

This account sfor binomial probbaility distribution with probbaility of success denoted by p, number of trials, n and specific number of successes in n trials, as r.

P(X,r)=nCr(p)^r(q)^n-r

4. a) P(X=6)=20C6(0.92)^6(0.08)^14=0.0000

b) P(X>=3)=1-P(X<3)=1-[P(X=0)+P(X=1)+P(X=2)]=1-[0.000+0.000+0.0001]=0.9999

5 a) P(X=7)=11C7(0.80)^7(0.20)^4=0.111

b) P(X>=7)=1-P(X<7)=1-0.050=0.950

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