Two letters are chosen at random with replacement from the word PROBABILITY. What is the chance that a) they are P and T i) in that order or ii) in either order b) They are both B's or they are different c) one is a B or an I and the other is neither a B nor an I

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Two letters are chosen at random with replacement from the word PROBABILITY. Note there are 11 letters in total in PROBABILITY.

a) P and T each only occur once in the word. The probability of choosing P and T in a particular order (eg P then T) is

Pr(PT) = Pr(P) x Pr(T) (as they are independent events)

= (1/11) x (1/11) = 1/121

There are only two orders the letters can be in: PT or TP, so the probability of P and T in any order is

Pr(PT) + Pr(TP) = 1/121 + 1/121 = 2/121

b) The probability of choosing 2 B's is

(2/11) x (2/11) = 4/121

There is only one order for choosing...

(The entire section contains 312 words.)

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