Question

Part 2: NO LINKS!! NOT MULTIPLE CHOICE! Please help me​

Answer 1

Answer:

(see attachment for tree diagram)

$\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}$

Part (a)

$\textsf{P(Head) and P(3)}=\sf \dfrac{1}{2} \times \dfrac{1}{6}=\dfrac{1}{12}$

Part (b)

$\textsf{P(Tail) and P(even)}=\sf \dfrac{1}{2} \times \dfrac{3}{6}=\dfrac{3}{12}=\dfrac{1}{4}$

Part (c)

$\textsf{P(not 6)}=\sf 1-\textsf{P(6)}=1-\dfrac{1}{6}=\dfrac{5}{6}$

$\implies \textsf{P(Head) and P(not 6)}=\sf \dfrac{1}{2} \times \dfrac{5}{6}=\dfrac{5}{12}$

Part (d)

As the six-sided die does not have a side labelled "7", the probability of rolling a 7 is zero.

$\implies \textsf{P(Head) and P(7)}=\sf \dfrac{1}{2} \times 0=0$