Examine each of the following statements and comment:(i) If two coins

1.	Examine each of the following statements and comment:(i) If two coins are tossed at the same time, there are 3 possible outcomes—two heads, two tails, or one of each. Therefore, for each outcome, the probability of occurrence is 1/3(ii) If a die is thrown once, there are two possible outcomes—an odd number or an even number. Therefore, the probability of obtaining an odd number is 1/2 and the probability of obtaining an even number is 1/2.
Answer» (i) Given statement is incorrect. If 2 coins are tossed at the same time, Total no. of possible outcomes = 4 {HH, HT, TH, TT} P(HH) = P(HT) = P(TH) = P(TT) = 1/4 {∵Probability = (No.of favorable outcomes)/(Total no.of possible outcomes)} i.e. for each outcome, probability of occurrence is 1/4 Outcomes can be classified as (2H, 2T, 1H & 1T) P(2H) = 1/4, P(2T) = 1/4, P(1H & 1T) = 2/4 Events are not equally likely because the event ‘one head & 1 tail’ is twice as likely to occur as remaining two. (ii) This statement is true When a die is thrown; total no. of possible outcomes = 6 {1, 2, 3, 4, 5, 6} These outcomes can be taken as even no. & odd no. P(even no.) = P(2, 4, 6) = 3/6 = 1/2 P(odd no.) = P(1,3,5) = 3/6 = 1/2 ∴ Two outcomes are equally likely

Examine each of the following statements and comment:(i) If two coins are tossed at the same time, there are 3 possible outcomes—two heads, two tails, or one of each. Therefore, for each outcome, the probability of occurrence is 1/3(ii) If a die is thrown once, there are two possible outcomes—an odd number or an even number. Therefore, the probability of obtaining an odd number is 1/2 and the probability of obtaining an even number is 1/2.

Answer»

(i) Given statement is incorrect. If 2 coins are tossed at the same time,

Total no. of possible outcomes = 4 {HH, HT, TH, TT}

P(HH) = P(HT) = P(TH) = P(TT) = 1/4 {∵Probability = (No.of favorable outcomes)/(Total no.of possible outcomes)}

i.e. for each outcome, probability of occurrence is 1/4

Outcomes can be classified as (2H, 2T, 1H & 1T) P(2H) = 1/4, P(2T) = 1/4, P(1H & 1T) = 2/4

Events are not equally likely because the event ‘one head & 1 tail’ is twice as likely to occur as remaining two.

(ii) This statement is true

When a die is thrown; total no. of possible outcomes = 6 {1, 2, 3, 4, 5, 6}

These outcomes can be taken as even no. & odd no.

P(even no.) = P(2, 4, 6) = 3/6 = 1/2

P(odd no.) = P(1,3,5) = 3/6 = 1/2

∴ Two outcomes are equally likely