In the following experiments write the sample space S, number of sample points n(S), events P, Q using set and n(P), n(Q). A coin is tossed and a die is thrown simultaneously: P is the event of getting head and an odd number. Q is the event of getting either H or T and an even number.

Solution:

Since a coins is tossed and a die is thrown simultaneously,

∴ Sample Space = {H1, H2, H3, H4. H5, H6, T1, T2, T3, T4, T5, T6}

∴ n(S) = 12

Let P = Event of getting head and an odd number.

P = {H1, H3, H5}

∴ n(P) = 3

Let Q = Event of getting either H or T and an even number

Q = {H2, H4, H6, T2, T4, T6}

∴ n(Q) = 6

In the following experiment write the sample space S, number of sample points n(S), events P, Q using set and n(P), n(Q). Form two digit number using the digits, 0, 1, 2, 3, 4, 5 without repeating the digits. P is the event that the number so formed is even. Q is the event that the number so formed is divisible by 3.

Solution:

Since two digit numbers are to be formed from the digits 0, 1, 2, 3, 4, 5 without repeating the digits.

∴ Sample Space = {10, 12, 13, 14, 15, 20, 21, 23, 24, 25, 30, 31, 32, 34, 35, 40, 41, 42, 43, 45, 50, 51, 52, 53, 54)

∴ n(S) = 25

Let P = Event that the number formed is even number.

∴ A = {10, 12, 14, 20, 24, 30, 32, 34, 40, 42, 50, 52, 54}

∴ n(P) = 13

Let Q = Event that the number so formed is divisible by 3

∴ Q = {12, 15, 21, 30, 42, 45, 51, 54}

∴ n(Q) = 8