Probability Test - 10

Probability of selecting a bulb from a bag,P(E) = 1/3

Probability of not selecting a bulb from bag,P(not E) = 1 - P(E) = 1 - 1/3 = 2/3

Total possibles outcomes = 20

Number of favourable outcomes of getting a multiple of 3 = { 3,6,9,12,15,18} = 6

Therefore, the the probability that the number is a multiple of 3 = 6/20= 3/10

The probability that a boy will get married to his girlfriend ,P(E) = 2/7

The probability that he will not get married to his girlfriend, P(not E) = 1 - P(E) = 1 - 2/7 = 5/7

Odds in favour are 2:5

This means the event can occur in 2 ways and there are 5 ways the event cannot occur

This means that there are 7 total outcomes and 2 are favourable

The probability of success 2 out of 7 = 2/7

Number of days in a non-leap year = 365 = 52 weeks and 1 day

Thus, the probability is to be calculated for the remaining 1 day.

That one day can be {Sun, Mon, Tues, Wed, Thurs, Fri, Sat}

Total number of outcomes = 7

Number of favourable outcomes = 1 (Since only one day is a Thursday)

Thus, the required probability of getting 53 thursdays in a non leap year = 1/7

Number of possible outcomes in in a simultaneous throw of 3 coins = { HHH, HHT, HTH, THH, HTT, THT, TTH, TTT } = 8

Number of favourable outcomes of getting two heads {HHT, HTH, THH} = 3

So,the probability of getting two heads in a simultaneous throw of 3 coins = 3/8

Total possible outcomes = 52

Number of favourable outcomes of getting a red King =2{ King of Diamonds or King of Hearts}

Probability of getting a red king from a deck of well shuffled 52 cards = 2/52 = 1/26

Number of possible outcomes when two dice are thrown = 36

Number of favourable outcomes of throwing a sum of 9 = {(3,6),(4,5),(5,4),(6,3)} = 4

The probability of throwing a sum of 9 = 4/36 = 1/9

When two different coins are tossed randomly, the sample space is given by

S = {HH, HT, TH, TT}

Therefore, n(S) = 4

Let E = event of getting no head.

Then, E = {TT} and, therefore, n(E) = 1. 
Therefore, P(getting no head) = P(E) = n(E) / n(S) = 1/4