Probability Test - 8

Total Number of Possible Choices = Number of ways in which one card can be drawn from the total 52 = 52

The gambler wins, if the card drawn is a spade or an ace.

Let , A : The event of the card drawn being a spade or an ace.

For event A,

There are 13 spades.

There are 4 aces, one of each type (spades, clubs, hearts and diamonds).

The 13 spades include the ace of spades. Thus there would be 3 aces (of clubs, hearts and diamonds in the remaining cards.)

The set of cards from which any card can appear to make the event a success would include the 13 spades and the 3 other aces.

Number of favorable/favourable choices = Number of ways in which one card which is a spade or an ace can be drawn from the total 16 = 16

Number of unfavorable choices = Total number of possible choices - Number of favorable choices = 52 - 16 = 36

Odds against the gambler winning the bet

⇒ Odds against the card drawn being a spade or an ace.

⇒ Odds against Event A = Number of unfavourable choices : Number of favorable choices = 36 : 16 = 9 : 4

When we toss three coins simultaneously then the possible of outcomes are: (HHH) or (HHT) or (HTH) or (THH) or (HTT) or (THT) or (TTH) or (TTT) respectively; where H is denoted for head and T is denoted for tail.

Therefore, total numbers of possible outcomes are 2³ = 8

Events of getting  2 heads and 1 tail = (HHT) ,(HTH) ,(THH) = 3

Therefore, number of favourable outcomes = 3

Therefore,the probability of getting 2 heads and 1 tail = 3/8

In tossing three coins, the sample space is given by
S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
And, therefore, n(S) = 8.

Let E = event of getting neither 3 heads nor 3 tails

Therefore, E ={HHT, HTH, THH, HTT, THT, TTH}

Therefore, n(E) = 6

Therefore, P(getting neither 3 heads nor 3 tails ) = P(E) = n(E) / n(S) = 6/8= 3/4

The probability of happening of an event  = 3/7

The probability of not happening of this event = 1 - 3/7 = 4/7

Total number of possible outcomes = 6

Number of favourable outcomes of getting prime numbers ={2, 3 ,5} = 3

Probability of getting a prime number = 3/6= 1/2