Question
A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability?
That the numbers obtained have a product less then $16$.
That the numbers obtained have a product less then $16$.
✓
Answer
Given: A pair of dice is thrown
To Find: Probability of the following:
Let us first write the all possible events that can occur
The numbers of obtained having a product less than $16 = 25$ i.e.,
To Find: Probability of the following:
Let us first write the all possible events that can occur
$(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),$
$(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),$
$(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),$
$(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),$
$(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),$
$(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),$
Hence total number of events is $6^2= 36$The numbers of obtained having a product less than $16 = 25$ i.e.,
$(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),$
$(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),$
$(3, 1), (3, 2), (3, 3), (3, 4), (3, 5),$
$(4, 1), (4, 2), (4, 3),$
$(5, 1), (5, 2), (5, 3),$
$(6, 1), (6, 2)$
$\therefore\ \text{Probability P(E)}=\frac{25}{36}$Need a full question paper?
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