Answer:
The conjecture is that the unit digit of 4^n = 4 when n = odd also 4^n = 6 when n = even
Step-by-step explanation:
The conjecture is that the unit digit of 4^n = 4 when n = odd also 4^n = 6 when n = even
To prove this conjecture
unit digit = 6
hence the property is true for ; n = 1 and n = 2 and also for every odd and even number ( i.e. from 1 to 8 )
Answer:
a) There are 9 outcomes.
b) **i have attached the tree diagram**
c) 1/9
d) 1/9
Step-by-step explanation:
Both events (choosing a shirt and choosing pants) are not mutually exclusive (disjoint). Meaning that both events can occur at the same time.
a) For a sequence of two events in which the first event can occur <em>m</em> ways and the second event can occur <em>n</em> ways, the events together can occur a total of <em>m</em> • <em>n</em> ways. So for this problem, you would do 3 • 3 which equals 9.
b) **tree diagram is attached**
c) Because there are two different events occurring (choosing a shirt and choosing pants) you need to multiply using the Multiplication Rule for Independent Events : P(A and B) = P(A) * P(B)
The probability of event A occurring (choosing a red shirt) is 1/3 and the probability of event B occurring (choosing brown pants) is also 1/3.
1/3 * 1/3 = 1/9
d) You would do the same thing here as part c.
The probability of event A occurring (choosing a blue shirt) is 1/3 and the probability of event B occurring (choosing blue pants) is again 1/3.
1/3 * 1/3 = 1/9
I hope this was helpful!! :)
