one die and a coin are tossed simultaneously, the probability of getting 5 on the top of the die and tail on the coin is: plz answer, plz,plz answer
Answers
Probability of any event is ratio of Number of chances for that event to occur to the number number of events.
Method 1:
Consider die and coin individually
Die
As a die have 6 face, and assuming that it is a normal die, the numbers will be from 1 to 6. There are two composite numbers in this set which are 4 and 6. so here the probability will be 2/6 i.e., 1/3
Coin
A coin has two sides head and tail. So the probability of getting a tail will be 1/2
As you mentioned composite number or tail, it will be union
Considering Die as D and Coin as C
P(D∪C)= P(D)+P(C)-P(D∩C)
=>P(D∪C)= 1/3+1/2–(1/2)*(1/3)
=>P(D∪C)=2/3
Here we have subtracted P(D∩C) because that event occurs with both D and C, as we have to consider it only once but we did add them twice in both P(D) and P(C) we have to subtract for once.
Method 2:
Consider all possible events and count them
1 T
2 T
3 T
4 T
5 T
6 T
1 H
2 H
3 H
4 H
5 H
6 H
Here the likely events are 8 and total events are 12, which means the probability is 8/12 i.e., 2/3
probability of tail on coin is 1/2 and probability of getting 5 on die is 1/6