Question

1) Three coins are tossed together. Find the probability of getting: (i) exactly two heads (ii) at most two heads (iii) at least one head and one tail (iv) no tails

2) A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is (a) either a black card or a king (b) black and a king (c) a jack, queen or a king (d) neither a heart nor a king (e) spade or an ace (f) neither an ace nor a king (g) neither a red card nor a queen (h) other than an ace

3) What is the probability that a number selected from the numbers 1, 2, 3…15 is a multiple of 4 ?

4). Cards marked with numbers 13, 14, 15,……. 60 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that, number on the card drawn is (i) divisible by 5 (ii) a number is a perfect square

5) In a simultaneous throw of a pair of dice, find the probability of getting. (a) 8 as the sum (b) a doublet (c) a doublet of prime numbers (d) a doublet of odd numbers (e) a sum greater than 9 (f) an even number on fir (g ) at least once (h)a number other than 5 on any dice. (i) even number on each die (j) 2 will come up at least once (k) 2 will not come either time

Answer 1

Answer:

When three coins are tossed together, the total number of outcomes =8

i.e., (HHH,HHT,HTH,THH,TTH,THT,HTT,TTT)

Solution (i):

Let E be the event of getting exactly two heads

Therefore, no. of favorable events, n(E)=3(i.e.,HHT,HTH,THH)

We know that, P(E) =(Total no.of possible outcomes)(No.of favorable outcomes)=83

Solution (ii):

Let F be the event of getting atmost two heads

Therefore, no. of favorable events, n(E)=7(i.e.,HHT,HTH,TTT,THH,TTH,THT,HTT)

We know that, P(F) =(Total no.of possible outcomes)(No.of favorable outcomes)=87

Solution (iii):